Segmentation Using Hybrid Discriminative Generative Label Fusion of Multiple Atlases

ABSTRACT

A method for segmenting a target image includes receiving the target image of an anatomical structure, registering a plurality of atlases to the target image, each of the atlases including an image and a plurality of labels corresponding to portions of the image, selecting a plurality of registered atlases, transferring the labels of selected registered atlases to the target image, combining the labels that are transferred to the target image using a fusion of a discriminative model and a generative model, and outputting a segmentation of the target image isolating the anatomical structure, wherein a segmentation of the target image is displayed.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 61/946,120, filed on Feb. 28, 2014, and U.S. ProvisionalPatent Application No. 62/077,230, filed on Nov. 8, 2014, the completedisclosures of which are herein expressly incorporated by reference intheir entirety for all purposes.

BACKGROUND

The present disclosure relates to methods for image segmentation, andmore particularly to a method for multi-atlas based segmentation.

Image segmentation is a process of partitioning an image into one ormore groups of pixels sharing certain characteristics. A group or groupsof pixels can delineate an object of interest. Image segmentationsimplifies the representation of an image and can be performed in twodimensions (2D) or three dimensions 3D.

In the context of medical imaging, accurate delineation of anatomicalstructures is critical for reliable quantitative analysis. For example,segmentation of left and right ventricles in cardiac images is aprerequisite for assessment of cardiac function (e.g., volumemeasurements, estimation of ejection fraction and myocardial motionanalysis) as well as diagnosis of various cardiac diseases. In clinicalroutines, the segmentation task is often performed manually, which istedious and time-consuming, in particular when dealing with very largenumber of scans, e.g., screening practice. Manual segmentation is alsodifficult to reproduce and suffers from inter and intra-observervariabilities.

BRIEF SUMMARY

According to an exemplary embodiment of the present invention, a methodfor segmenting a target image includes receiving the target image of ananatomical structure, registering a plurality of atlases to the targetimage, each of the atlases including an image and a plurality of labelscorresponding to portions of the image, selecting a plurality ofregistered atlases, transferring the labels of selected registeredatlases to the target image, combining the labels that are transferredto the target image using a fusion of a discriminative model and agenerative model, and outputting a segmentation of the target imageisolating the anatomical structure.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

Preferred embodiments of the present invention will be described belowin more detail, with reference to the accompanying drawings:

FIG. 1 is a flow diagram of a multi-atlas segmentation method accordingto an exemplary embodiment of the present invention;

FIG. 2 is a flow diagram of a method for generative modeling in a labelfusion method according to an exemplary embodiment of the presentinvention;

FIG. 3 is a flow diagram of a method for discriminative modeling in alabel fusion method according to an exemplary embodiment of the presentinvention; and

FIG. 4 is a diagram of a computer system configured for multi-atlassegmentation according to an exemplary embodiment of the presentinvention.

DETAILED DESCRIPTION

According to an exemplary embodiment of the present invention, aplurality of labeled atlases are registered to a target image. Thelabels of the atlases are transferred to each pixel the target image,such that each pixel can be associated with labels from differentatlases. The transferred labels of each pixel of the target image arefused using a discriminative model and a generative model to determine asynergistic label for each pixel and resulting in segmentation of thetarget image.

Embodiments of the present invention are applicable to fields includingmedical imaging for segmenting one or more objects of interest in atarget image of anatomy. The object(s) of interest can include the leftand right ventricles of a heart, fibroglandular tissue or adipose tissueor fat in breast tissue, the hippocampus in a brain, etc. Otherexemplary fields include quantitative analysis of anatomical functions,such as cardiac function, brain function, etc., and the diagnosis ofdisease.

For example to segment heart anatomies (e.g., left ventricle and rightventricle), the heart atlases where heart anatomies are labeled areused. Similarly, to segment brain parts (e.g., hippocampus, cerebrallobe), the brain atlases where the brain parts are labeled are used.

Referring to FIG. 1, according to an exemplary embodiment of the presentinvention, a multi-atlas segmentation can be performed in a 2D image(e.g., 2D brain scan) or a 3D volume (e.g., cardiac magnetic resonanceimaging (MRI)). Hereinafter, “target image” will be used as a generalterm meaning either 2D image or 3D volume, unless expressly notedotherwise. The multi-atlas segmentation combines a discriminative methodand a generative learning method to label pixels of the target image. Asshown in FIG. 1, a segmentation method 100 includes atlas generation104, registration 101, atlas selection 106, a label fusion framework107, and post processing 111.

During atlas generation 104, one or more anatomical structures ofinterest are labeled in a set of images or volumes. The labeling of theanatomical structures of interest can be performed manually by domainexperts, e.g., clinicians or radiologist. More particularly, the imagesare labeled by label l to identify anatomical structures such as leftventricle, a right ventricle a right atrium and a left atrium in acardiac image. In one or more embodiments of the present invention, thelabels are represented in an image format where pixels of an anatomicalstructure share the same value, e.g., “LV” for pixels corresponding tothe left ventricle. An image and its corresponding labels comprise anatlas.

It should be understood that embodiments of the present invention arenot limited to manual labeling, and other methods can also be used(e.g., semi-automated labeling).

During registration 101, each atlas 103 is registered against a giventarget image 102. The registration 101 can be performed using one ormore registration techniques, such as a rigid registration, an affineregistration, and a deformable registration. The registration 101 givesa correspondence between the target image 102 and each of the atlases103. In one or more embodiments of the present invention, thecorrespondence is determined pixel-to-pixel. According to one exemplaryembodiment of the present invention, in a case where a target image andan atlas image have different resolution, the pixels in atlas image areresampled to match the resolution of the target image. Thecorrespondence is used to generate a plurality of registered atlases 105for the target image 102 and to transfer the labels from each atlas tothe target image.

According to an exemplary embodiment of the present invention, one ormore registered atlases are selected at 106. More particularly, katlases are selected for the target image from the registered atlases105 using one or more features of the images (e.g., intensity, texture,etc.), where k is a positive integer. These features can be differentcriteria and/or attributes. For example, the correlation of pixelintensity between the target image and the atlas images around theanatomical structure of interest can be one criteria.

To perform the selection 106, a feature similarity between eachregistered atlas and the target image is determined and a rank R1 foreach atlas is obtained, where a low rank is given to an atlas similar tothe target image and a high rank to a dissimilar atlas. Further, afeature distance (such as Normalized Correlation Coefficient, Sum ofSquared distance, etc., between the pixels in the atlas image and thetarget image can be used) between each of the registered atlases and thetarget image is determined. Each atlas is assigned a rank value R2,where a low rank is assigned to a similar atlas and a high rank isassigned to a dissimilar atlas. According to an embodiment of thepresent invention, a combined score for an atlases image is defined asthe R1+R2. The k atlases with the smallest final scores can be selected.

One of ordinary skill in the art would appreciate that differentrankings and selection criteria can be used without departing from thescope of the present disclosure.

In an atlas label fusion framework 107, the labels of each of theatlases obtained from the atlas selection 106 are combined to obtainfused labels for the target image. According to an embodiment of thepresent invention, a label fusion framework 107 uses a hybrid of adiscriminative method and a generative method. The label fusionframework 107 includes discriminative training 108, generative modellearning 109, and a fusion of the discriminative and generative models110.

A discriminative model, which is a probabilistic classifier, is trained108 in a local window using atlas patches as training samples. Thediscriminative model acts as a prior model p(l) and gives an initialhypotheses of the label l in terms of a first score. The label l isindexed to the objects (e.g., l=1 refers to Right ventricle and l=2refers to Left ventricle in a heart) to be segmented in the targetimage.

A probability distribution function is trained for each label (e.g.,left ventricle, right ventricle, etc.) as a generative model 109. Forexample, in the context of a cardiac image, the class labels can include“LV” for left ventricle, “RV” for right ventricle, “RA” for rightatrium, “LA” for left atrium, etc. The generative model gives alikelihood value for the given feature (such as raw intensity values,histogram of oriented gradients or wavelets computed inside an imagepatch), in terms of a second score, that is, each label is associatedwith a likelihood value.

According to an exemplary embodiment of the present invention, the firstscore from the probabilistic classifier, used as a label prior, and thesecond score from the generative model are combined using a Bayesianrule at 110, wherein the hypothesis obtained from the probabilisticclassifier is verified by the generative model p(f/l). The Bayesian ruleis a patch-likelihood-based generative model outputting a fused score,which is a synergistic combination of the first score from theprobabilistic classifier and the second score related to the featurelikelihood.

The label fusion framework 107 combines the power of discriminativelearning and generative modeling in a single framework to exploitcomplementary properties of the individual approaches. This hybridapproach to label fusion results in good segmentation performance androbustness by implicitly verifying the first scores from discriminativemodel 108 using the likelihood values or second scores from thegenerative model 109 in a Bayesian label fusion 110.

According to one or more embodiments of the present invention, allatlases include all of the objects to be segmented. Given a targetimage, each atlas image is registered to the target image. If there areN atlases, then after registration, N registered atlases are generated.Given registered atlases, the best K atlases are selected. The labelfusion combines the labels from the selected registered atlases. In thiscontext, if each atlas has 5 labeled objects, then the output of labelfusion is the segmentation of the 5 objects.

Referring to FIGS. 2 and 3, atlas label fusion framework 107 combinesthe label of the selected atlas to obtain the target label beforepost-processing 111. For each pixel of the target image, adiscriminative model is trained 108 according to FIG. 2 and a generativemodel is trained 109 according to FIG. 3.

Referring to FIG. 2, according to one or more embodiments of the presentinvention, a set of feature vectors are determined around theneighborhood of the pixel in the corresponding atlases and the label ofthe pixel is assigned to each feature vector 201. According to one ormore embodiments of the present invention, the feature vector can beextracted from image intensities, image gradients, wavelets, etc., fromthe local patch. A probabilistic classifier is trained 202 using theextracted training feature in the local neighborhood (e.g., a 2×2×2neighborhood, a 3×3×3 neighborhood, etc.) to predict a label for thetarget image pixel 203. Classifiers such as random forest, supportvector machine, and neural networks can be used. It should be understoodthat the local neighborhood can be sized according to an application andthat the application is not limited to any particular sizedneighborhood.

According to one or more embodiments of the present invention, to trainthe generative model 109 according to FIG. 3, the dimension of thefeature vectors determined at 301 is reduced at 302 using a principalcomponent analysis to filter out noise in the feature vectors. (Itshould be understood that features extracted at 201 and 301 can bedifferent, but they are determined from the same local neighborhood ofthe target image and selected registered atlas images). The relativelocation of a center of an image patch is also included in the featurevector. The relative location is determined with respect to the targetpixel location. In 303, a feature set is grouped into several featuresubsets according to the label each subset contains and a probabilitydistribution function is trained on each feature subset at 304 todetermine target pixel likelihoods at 305. Modeling techniques (such asGaussian mixture model, Kernel density estimation, etc.) can be used totrain the probability distribution function for each label.

The probability score from the discriminative model and the likelihoodscore from the generative model are combined at 110. More particularly,the feature vectors on a patch centered at a pixel of the target imageare extracted as in 301 (FIG. 3). The classification scores of thefeature vectors using the trained classifier from 203 (FIG. 2). Thistrained classifier gives the prior probability p(l) of each label forthe pixel. The likelihood score of the feature for each label isdetermined using the probability distribution function trained at 305.This probability distribution function outputs the likelihood p(f/1) ofthe feature determined at the pixel for each label. A final posteriorprobability of the label at the pixel is determined at 110 using aBayesian equation p(l/f)=(p(f/l)*p(l)/C, where C is a constant that canbe determined by summing the term p(f/l)*p(l)) for all labels.

According to an embodiment of the present invention, in the postprocessing 111, over segmentation is used to remove spurioussegmentation around label boundaries and outliers. Over segmentationgroups pixels that are spatially closer and that share a similarappearance into a patch called super-pixel. Thus, a group of pixelsinside the super-pixel share similar pixel characteristics. For eachsuper-pixel, a histogram from the posterior probability of pixels isdetermined. Then all pixels inside the super-pixel are assigned to thelabel with a largest histogram value. The post processing 111 canfurther include the display of an image of a segmented object, such as aheart, left or right ventricles, portions of a brain etc.

By way of recapitulation, according to an exemplary embodiment of thepresent invention, a method for segmenting a target image includesreceiving the target image of an anatomical structure 102, registering aplurality of atlases to the target image 101, each of the atlasesincluding an image and a plurality of labels corresponding to portionsof the image, transferring the labels of registered atlases to thetarget image 106, combining the labels that are transferred to thetarget image using a fusion of a discriminative model and a generativemodel 107, and outputting a segmentation of the target image isolatingthe anatomical structure, wherein a segmentation of the target image isdisplayed 111. The anatomical structure can include a left ventricle ofheart and a right ventricle of heart, fibroglandular tissue or fat inbreast images, a hippocampus in the brain, etc.

Throughout the present disclosure, it should be understood that the term“pixel” includes one or more pixels and voxels, whether in 2D or 3D.

The methodologies of embodiments of the disclosure may be particularlywell-suited for use in an electronic device or alternative system.Accordingly, embodiments of the present invention may take the form ofan entirely hardware embodiment or an embodiment combining software andhardware aspects that may all generally be referred to herein as a“processor,” “circuit,” “module” or “system.”

Furthermore, it should be noted that any of the methods described hereincan include an additional step of providing a system for feedbackcollection and analysis. Further, a computer program product can includea tangible computer-readable recordable storage medium with code adaptedto be executed to carry out one or more method steps described herein,including the provision of the system with the distinct softwaremodules.

Referring to FIG. 4; FIG. 4 is a block diagram depicting an exemplarycomputer system 400 for multi-atlas based segmentation according to anembodiment of the present invention. The computer system shown in FIG. 4includes a processor 401, memory 402, display 403, input device 404(e.g., keyboard), a network interface (I/F) 405, a media IF 406, andmedia 407, such as a signal source, e.g., camera, Hard Drive (HD),external memory device, etc.

In different applications, some of the components shown in FIG. 4 can beomitted. The whole system shown in FIG. 4 is controlled by computerreadable instructions, which are generally stored in the media 407. Thesoftware can be downloaded from a network (not shown in the figures),stored in the media 407. Alternatively, software downloaded from anetwork can be loaded into the memory 402 and executed by the processor401 so as to complete the function determined by the software.

The processor 401 may be configured to perform one or more methodologiesdescribed in the present disclosure, illustrative embodiments of whichare shown in the above figures and described herein. Embodiments of thepresent invention can be implemented as a routine that is stored inmemory 402 and executed by the processor 401 to process the signal fromthe media 407. As such, the computer system is a general-purposecomputer system that becomes a specific purpose computer system whenexecuting routines of the present disclosure.

Although the computer system described in FIG. 4 can support methodsaccording to the present disclosure, this system is only one example ofa computer system. Those skilled of the art should understand that othercomputer system designs can be used to implement embodiments of thepresent invention.

The present invention may be a system, a method, and/or a computerprogram product. The computer program product may include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, or either source code or object code written in anycombination of one or more programming languages, including an objectoriented programming language such as Smalltalk, C++ or the like, andconventional procedural programming languages, such as the “C”programming language or similar programming languages. The computerreadable program instructions may execute entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer may be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection may be made to an external computer(for example, through the Internet using an Internet Service Provider).In some embodiments, electronic circuitry including, for example,programmable logic circuitry, field-programmable gate arrays (FPGA), orprogrammable logic arrays (PLA) may execute the computer readableprogram instructions by utilizing state information of the computerreadable program instructions to personalize the electronic circuitry,in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the block may occur out of theorder noted in the figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

Although illustrative embodiments of the present invention have beendescribed herein with reference to the accompanying drawings, it is tobe understood that the invention is not limited to those preciseembodiments, and that various other changes and modifications may bemade therein by one skilled in the art without departing from the scopeof the appended claims.

1. A method for segmenting a target image comprising: receiving thetarget image of an anatomical structure; registering a plurality ofatlases to the target image, each of the atlases including an image anda plurality of labels corresponding to portions of the image; selectinga plurality of registered atlases; transferring the labels of selectedregistered atlases to the target image; combining the labels that aretransferred to the target image using a fusion of a discriminative modeland a generative model; and outputting a segmentation of the targetimage isolating the anatomical structure, wherein a segmentation of thetarget image is displayed.
 2. The method of claim 1, further comprisinggenerating the plurality of atlases, wherein the portions of the imagecorrespond to the anatomical structure.
 3. The method of claim 1,wherein the registration is on a pixel-to-pixel correspondence betweenthe atlases and the target image.
 4. The method of claim 1, wherein theselection of the plurality of the registered atlases uses a criteria forselection.
 5. The method of claim 4, further comprising: determining afeature similarity between each of the registered atlases and the targetimage; determining a first ranking each of the registered atlasesaccording to the feature similarities; determining a feature distancebetween each of the registered atlases and the target image; determininga second ranking each of the registered atlases according to the featuredistances; and selecting the registered atlases using the first rankingand the second ranking, wherein the feature similarity and the featuredistance are the criteria for selection.
 6. The method of claim 1,further comprising determining the discriminative model.
 7. The methodof claim 6, further comprising: extracting a feature vector of a localneighborhood around each pixel of the atlases; and training aprobabilistic classifier using the feature vectors.
 8. The method ofclaim 1, further comprising determining the generative model.
 9. Themethod of claim 8, further comprising: extracting a feature vector of alocal neighborhood around each pixel of the atlases; reducing adimension of the feature vectors; adding a relative location to thefeature vectors; grouping the feature vectors according to the labels;training a probability distribution function on a feature vector set ofeach of the labels; and determining a target pixel likelihood using theprobability distribution function.
 10. The method of claim 1, whereinthe combination of the labels comprises: extracting a feature vector ona patch centered at a given pixel on the target image; determining aclassification score of the feature vector using a classifier of thediscriminative model, which outputs a prior probability p(l) of eachlabel l for the given pixel; determining a likelihood score of thefeature vector for each label using a probability distribution functionof the generative model, which outputs a likelihood p(f/l) of thefeature vector f determined at the given pixel for each of the labels;and determining a posterior probability of a label at the given pixelusing a Bayesian rule as p(l/f)=(p(f/l)*p(l)/C, where C is a constantdetermined by summing a term p(f/l)*p(l)) for all labels.
 11. A computerprogram product for segmenting a target image, the computer programproduct comprising a computer readable storage medium having programinstructions embodied therewith, the program instructions executable bya processor to cause the processor to perform a method comprising:receiving the target image of an anatomical structure; registering aplurality of atlases to the target image, each of the atlases includingan image and a plurality of labels corresponding to portions of theimage; selecting a plurality of registered atlases; transferring thelabels of selected registered atlases to the target image; combining thelabels that are transferred to the target image using a fusion of adiscriminative model and a generative model; and outputting asegmentation of the target image isolating the anatomical structure. 12.The computer program product of claim 11, further comprising generatingthe plurality of atlases, wherein the portions of the image correspondto the anatomical structure.
 13. The computer program product of claim11, wherein the registration is on a pixel-to-pixel correspondencebetween the atlases and the target image.
 14. The computer programproduct of claim 11, wherein the selection of the plurality of theregistered atlases uses a criteria for selection.
 15. The computerprogram product of claim 14, further comprising: determining a featuresimilarity between each of the registered atlases and the target image;determining a first ranking each of the registered atlases according tothe feature similarities; determining a feature distance between each ofthe registered atlases and the target image; determining a secondranking each of the registered atlases according to the featuredistances; and selecting the registered atlases using the first rankingand the second ranking, wherein the feature similarity and the featuredistance are the criteria for selection.
 16. The computer programproduct of claim 11, further comprising determining the discriminativemodel.
 17. The computer program product of claim 16, further comprising:extracting a feature vector of a local neighborhood around each pixel ofthe atlases; and training a probabilistic classifier using the featurevectors.
 18. The computer program product of claim 11, furthercomprising determining the generative model.
 19. The computer programproduct of claim 18, further comprising: extracting a feature vector ofa local neighborhood around each pixel of the atlases; reducing adimension of the feature vectors; adding a relative location to thefeature vectors; grouping the feature vectors according to the labels;training a probability distribution function on a feature vector set ofeach of the labels; and determining a target pixel likelihood using theprobability distribution function.
 20. The computer program product ofclaim 11, wherein the combination of the labels comprises: extracting afeature vector on a patch centered at a given pixel on the target image;determining a classification score of the feature vector using aclassifier of the discriminative model, which outputs a priorprobability p(l) of each label l for the given pixel; determining alikelihood score of the feature vector for each label using aprobability distribution function of the generative model, which outputsa likelihood p(f/l) of the feature vector f determined at the givenpixel for each of the labels; and determining a posterior probability ofa label at the given pixel using a Bayesian rule asp(l/f)=(p(f/l)*p(l)/C, where C is a constant determined by summing aterm p(f/l)*p(l)) for all labels.